ISSC 2004, Belfast, June 30 - July 2
Characterisation of Schottky Varactor Diodes for Pulse
Compression Circuits
Falah Mohammed , David Linton 

High Frequency Electronics Group,
School of Electrical and Electronic Engineering
Queen’s University,
Belfast, Northern Ireland, BT9 5AH
UK
E-mail: f.mohammed@ee.qub.ac.uk
d.linton@ee.qub.ac.uk
__________________________________________________________________________________________
Capacitance (f F)
Abstract – The application of a non-linear lumped element circuit
model for Schottky varactor diodes is presented in this paper. The
nonlinear parameters of the GaAs varactor diode are extracted
using small and large signal measurements. The modelled and
measured results show strong agreement.
__________________________________________________________________________________________
Different techniques are proposed for this purpose
including equalization techniques [2]. An alternative
solution using nonlinear wave transmission to
I. INTRODUCTION
compensate for the dispersion problem has been
The need to transmit multigigabit data streams within
reported [3] using Non-Linear Transmission Line
optical networking equipment, such as routers and
Technology (NLTL). The NLTL can compensate for
switches, is driving the need to increase the
dispersion by providing different propagation speeds
aggregate bandwidth through a copper medium. The
for the harmonic contents of the digital bit stream. It
dispersion and attenuation in the copper medium
can also regenerate the attenuated or lost harmonics
increases significantly with the increase in
due to the low pass filter properties of the digital
transmission frequency. The large increase in
interconnects.
dispersion and attenuation which accompanies the
The NLTL uses the non-linear CV characteristics of
increase of the transmission frequency is a bottle
the shunt mounted Schottky diode to achieve
neck that limits the bandwidth in electro-optic
nonlinear wave propagation properties. Typical C-V
backplane systems. Typical dispersion and
characteristics for the Schottky diode are shown in
attenuation on FR4 multilayer printed circuit board
Figure 1.
(PCB) is 0.9 dB/in and 1.2 ps/in respectively
[1]. With the large improvement of the bandwidth
500
which has extended to more than 10 Gbits/s for the
400
CV Characteristics
OC192 standard, the communication channel
designers now consider every single element in the
300
communication channel. Signal distortion arising
200
from attenuation and dispersion problems in the
multilayer PCB in the electro-optic backplane can
100
lead to significant inter-symbol interference (ISI).
The ISI is increased by the multiple reflections and
0
the low pass filter properties of the chip
-8
-7
-6
-5
-4
-3
-2
-1
0
interconnects in the backplane card which causes the
Bias Voltage (V)
loss of the high frequency components of the digital
Figure 1 The Schottky diode CV characteristics.
bit stream.
To overcome this problem a digital bit stream is
The schematic diagram and circuit diagram of the
demultiplexed in the time domain to transmit the
NLTL are shown in Figure 2.
data at slower speeds and therefore reduce the
In this paper the Schottky diode equivalent circuit
distortion problems associated with the increase of
model which is extensively used to study Schottky
the transmission frequency.
diode mixer [4]-[5] properties is used to model the
Schottky diode for NLTL applications. The full
nonlinear Schottky diode model is presented in this
paper. Nonlinear characterization of the Schottky
diode equivalent circuit parameters based on small
and large signal measurements are also given.
Analysis has been performed on two devices the
Bookham 6×100 µm2 (device 1) and the OMMIC 3 
40 µm (device 2) Schottky varactor diode.
IV. SMALL SIGNAL MEASUREMENTS
Small signal measurements were performed using
the HP-8510B Vector Network Analyser (VNA)
using the setup shown in Figure 4.
HP-8510
GPIB Bus
8510B
Coaxial Cables
(a)
Personal
Computer
Probe
station
Synthesised
sweeper
(b)
Figure 2 (a) Schematic diagram and (b) the equivalent
circuit of the NLTL.
II. SCHOTTKY DIODE MODEL
Basically the Schottky diode can be modelled by a
nonlinear junction capacitance in parallel with a
nonlinear junction conductance. The nonlinear
capacitance models the Schottky diode under reverse
bias conditions while the junction conductance
models the diode under forward bias conditions. For
accurate modelling, a series resistance and series
inductance are considered in the Schottky diode
equivalent circuit model. The Schottky diode
equivalent circuit model is shown in Figure 3.
Gj
Rs
S-parameter
Test set
Ls
Cj
Figure 3 The equivalent circuit model of the Schottky
varactor diode.
III. SCHOTTKY DIODE PARAMETER
EXTRACTION
The junction capacitance and the series resistance are
the important parameters for the NLTL design.
These two elements are extracted using small signal
measurements under reverse bias conditions. The
junction conductance is less important for the NLTL
but it is extracted using DC measurements under
forward bias conditions.
The Schottky diode model is verified using large
signal measurements.
Figure 4 Small signal measurement setup
The system was calibrated using the Line Reflect
Match (LRM) technique to eliminate the systematic
errors from the S-parameter measurement system.
The LRM calibration technique requires the use of
three calibration standards to transfer the Sparameter measurement plane to the probe tips. The
standards are:
1. The reflect standard is either an open or
short circuit. The open is preferred because
the probe tips are left in air and no probe
placement error occurs.
2. The match load standard is two separated
50  loads.
3. Thru line standard which is a 50 
m
length CPW line providing 1 ps electrical
delay.
Port extensions of 0.5 ps are added to each port to
compensate for the delay caused by the thru line at
each probe tip. The calibration standards are
available on the Impedance Standard Substrate (ISS)
with gold contacts and Ground Signal Ground (GSG)
configuration.
Devices 1 and 2 were measured using the Cascade
12000TM probe station where Rigid GSG 150 m
Cascade probes are used for probing the cathode and
anode pads of each Schottky diode. Reverse DC bias
was applied to the device under test using the bias
tee on the VNA. A photograph showing probe heads
contacting the measurement pads is shown in Figure
5.
profile can be approximated by hyperbolic curve
fitting as reported by [6]. The non-linearities of the
diode can be modelled by
212
(1)
C d (V ) 

V 

1 

 0.6 
where  is the nonlinearity constant which depends
on the doping profile of the Schottky diode. Larger
nonlinear characteristics can be achieved if this
constant is increased. Increasing the value of  is
limited to the fabrication process of the Schottky
diode. The value of this constant for device 1 is (  =
0.7)
Device 1
V=2V
V=0V
Ohmic
Device 2
Schottky Contact
Depletion region
The measured reflection coefficient S11 of device 1 at
different reverse bias points is shown in Figure 6.
Ohmic
Schottky Contact
Depletion region
Ohmic
N- active layer
N- active layer
Figure 5 Probe heads contacting the measurement
pads for device 1 and device 2.
Ohmic
Figure 7 Cross section view of the Schottky diode shows
the Schottky contact and the depletion region.
For reverse bias voltages larger than 2V, the
depletion region is almost fully depleted. If the
depletion layer is fully depleted then the diode
parameters are almost constant, therefore the
reflection coefficient S11 will be almost constant and
does not change with bias.
Freq = 1.044 GHz
Freq = 40 GHz
Bias -2 V
Bias 0 V
Freq = 1.044 GHz
Bias -1 V
Freq = 40 GHz
Bias 0 V
Bias -1 V
Bias -3 V
freq (1.044 GHz to 40.00 GHz)
Bias -2 V
Figure 6 Measured reflection coefficient S11 for device 1
Schottky varactor diode at different bias points.
Figure 6 shows that the capacitance is the dominant
parameter of device 1 as the measured reflection coefficient is in the lower half of the smith chart. It can
also be noticed from the figure that the reflection
coefficient is affected by the reverse bias voltage as
it is varied from (0 to 2V). Further increase in the
reverse bias voltage has only a small effect on the
measured reflection coefficient S11.
This is because the depletion region under the
Schottky contact experiences large non-linear
characteristics as the bias is varied from (0 to 2V)
because of the hyper-abrupt doping profile [6], Figure
7. This profile experiences large non-linearities
because of the non-uniform charge distribution under
the Schottky contact which is approximated by a
Gaussian distribution [6]. The hyper-abrupt doping
Bias -3 V
freq (1.044 GHz to 40.00 GHz)
Figure 8 Measured reflection coefficient S11 for device 2
Schottky varactor diode at different bias points.
The measured reflection coefficient for device 2 is
shown in Figure 8.
The measured reflection coefficient S11 of device 2
shows similar observations as for those of device 1
(i.e. the diode has capacitive properties and the diode
parameters vary as the voltage is varied from 0 to 2
V). The reason for this is that the depletion region
exhibits strong nonlinear characteristics for voltages
ranging from 0 to 2V. For voltages more negative
than 2V the depletion region is almost fully
depleted, therefore the diode characteristics are
almost constant; hence the reflection coefficient is
constant.
A comparison between Figure 6 and Figure 8 shows
the reflection coefficient curves for device 1 are
different from those for device 2. The reason for this
difference is in the doping profile. Device 1 uses a
hyper-abrupt doping profile [7] whereas device 2
uses a delta-doped profile [8].
The series resistance of the Schottky diode is
extracted from the reflection coefficient (S11), where
it is the real part of the reflection coefficient
according to equation (1)
Figure 10 shows that device 2 has larger nonlinear
characteristics between the reverse bias voltage
range  V to 2 V compared with device 1. The
reason for that again refers to the delta-doping
profile used in the device 2 foundry process.
(2)
Rs  real (S11 )
The reflection coefficient is a function of the
DCbias, and the series resistance is also a function
of the DC bias. Because the Schottky diode
resistance depends on frequency (skin effect which is
basically in the metallization layers of the Schottky
diode), the resistance is extracted at 5 GHz as a
figure of merit. The series resistance of device 1 was
5.71  while it was 6.95  for device 2.
The junction capacitance and the series inductance
are extracted based on an ABCD matrix technique.
The extracted CV characteristic and series resistance
for both diodes are given in Figure 9.
   qV j  
 nKT

(3)
I d  I s  e    1




where Id is the Schottky diode current, Vj is the
voltage across the junction conductance, Is is the
saturation current, K is the Boltzmann constant, T is
the absolute temperature and q is the electron charge.
The measured IV characteristics for both device 1
and device 2 Schottky varactor diodes are shown in
Figure 11.
250
200
150
100
0.45
0.4
50
Current (A)
300
Capacitance (fF)
350
device 2
The junction conductance of the Schottky diode is
extracted from the IV measurements. The IV
characteristics of the Schottky diode are given by
equation 3 [9].
device 1
0.35
400
device 1
V. IV-CHARACTERISTICS.
device 2
0.3
0.25
0.2
0.15
0.1
0.05
0
0
0.1
0.2
0.3
Voltage (V)
0.4
0.5
0.6
0
-9.6
-7.6
-5.6
-3.6
-1.6
Figure 11 Measured IV characteristics for device 1 and
device 2 Schottky varactor diodes.
0.4
Voltage (V)
Figure 9 The extracted CV characteristics for both device 1
and device 2 Schottky varactor diodes.
Device 2 has larger nonlinearity compared with the
device 1 since the capacitance of device 2 changes
sharply over a smaller voltage range compared to
device 1. The reason for this difference in
nonlinearity is the difference in the doping profile
where device 1 uses hyper-abrupt and device 2 uses a
delta-doped profile.
VI. LARGE SIGNAL MEASUREMENTS.
150
100
device 1
50
Inducatnce (pH)
250
200
device 2
0
-8
-6
-4
-2
Figure 11 shows that device 1 has much larger
current compared to device 2 because device 1 has
larger area compared to device 2.
The ideality factor (n) and the saturation current are
extracted based on the procedures outlined in [10].
The ideality factor (n) for device 1 was 1.2 compared
to 1.09 for device 2.
The saturation current for device 1 was 3 pA
compared to 2.5 pA for device 2.
0
Bias Voltage (V)
Figure 10 Extracted series inductance for device 1 and
device 2 Schottky varactor diodes.
The extracted Schottky diode model for both device
1 and device 2 was verified using large signal
measurements. The large signal measurement system
was calibrated to transfer the measurement reference
plane to the probe tips for accurate measurements. A
large signal with variable input power is injected
through each Schottky varactor diode. The input
signal frequency was 1 GHz and the diode was
reverse biased at 1 V. The power of the
fundamental and the second harmonic were
measured using the Microwave Transition Analyser
(MTA). The measured results are compared with the
ADSTM harmonic balance (HB) simulation
performed on the extracted model for device 1 and
device 2.
The measured and simulated (using ADSTM)
fundamental and second harmonic power of device 1
and device 2 are shown in Figure 12 and Figure 13
respectively.
0
-5
Device 2 shows stronger nonlinearities in the
extracted parameters because of its delta doping
profile compared to device 1 which uses a hyperabrupt doping profile.
The extracted Schottky diode model for both diode
types was verified to the actual Schottky diode
device by large signal measurements. The measured
and modelled results show good agreement
indicating that the nonlinear circuit model for device
1 and device 2 was successfully extracted.
O/P Power (dBm)
-10
VIII.
-15
-2 0
This project has been supported financially by
Solectron/C-MAC. The Schottky diodes were
donated by Bookham and OMMIC.
Freq . = 1 GHz, Bias = -1V
-2 5
-3 0
mo d eled fund amental
mo d eled s ec. har.
-3 5
-4 0
meas ured fund amental
meas ured s ec. har.
-4 5
ACKNOWLEDGMENT
IX. REFERENCES
-50
5
6
7
8
9
10
11
12
13
14
Input P o we r (dB m )
Figure 12 Measured and simulated fundamental and
second harmonic powers for device 1 Schottky varactor
diode.
0
O/P Power (dBm)
-5
Freq . = 1 GHz, Bias = - 1V
-10
-15
-2 0
-2 5
-3 0
mo d eled fund amental
-3 5
mo d eled s ec. har.
-4 0
meas ured fund amental
-4 5
meas ured s ec. har.
-50
5
6
7
8
9
10
11
12
13
14
Input power (dBm)
Figure 13 Measured and simulated fundamental and
second harmonic powers for device 2 Schottky varactor
diode.
Measurement shows good agreement with the
simulated results for both device 1 and device 2 as
shown in Figure 12 and Figure 13 respectively.
VII.
CONCLUSION
The non-linear equivalent circuit model for the
Schottky varactor diode is extracted. This model is
an important step in the design of the NLTL circuit
which is used for pulse compression circuit
applications.
Small signal measurements were bias dependent
because the CV characteristics and the IV
characteristics of the Schottky diode are bias
dependent. The small signal measurements were bias
dependent only up to 2 V for both device 1 and
device 2. This is because the depletion region is fully
depleted for bias voltages larger than 2 V, therefore
equivalent circuit parameters become constant.
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